CN115840187A - Multi-stage angle-of-arrival estimation in a vehicle radar system - Google Patents

Multi-stage angle-of-arrival estimation in a vehicle radar system Download PDF

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CN115840187A
CN115840187A CN202211095927.9A CN202211095927A CN115840187A CN 115840187 A CN115840187 A CN 115840187A CN 202211095927 A CN202211095927 A CN 202211095927A CN 115840187 A CN115840187 A CN 115840187A
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antenna elements
ula
elevation angles
ura
processing circuitry
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O.巴尔沙洛姆
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GM Global Technology Operations LLC
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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
    • G01S13/00—Systems using the reflection or reradiation of radio waves, e.g. radar systems; Analogous systems using reflection or reradiation of waves whose nature or wavelength is irrelevant or unspecified
    • G01S13/66—Radar-tracking systems; Analogous systems
    • G01S13/68—Radar-tracking systems; Analogous systems for angle tracking only
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
    • G01S13/00—Systems using the reflection or reradiation of radio waves, e.g. radar systems; Analogous systems using reflection or reradiation of waves whose nature or wavelength is irrelevant or unspecified
    • G01S13/88—Radar or analogous systems specially adapted for specific applications
    • G01S13/93—Radar or analogous systems specially adapted for specific applications for anti-collision purposes
    • G01S13/931—Radar or analogous systems specially adapted for specific applications for anti-collision purposes of land vehicles
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
    • G01S13/00—Systems using the reflection or reradiation of radio waves, e.g. radar systems; Analogous systems using reflection or reradiation of waves whose nature or wavelength is irrelevant or unspecified
    • G01S13/02—Systems using reflection of radio waves, e.g. primary radar systems; Analogous systems
    • G01S13/06—Systems determining position data of a target
    • G01S13/42—Simultaneous measurement of distance and other co-ordinates
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
    • G01S13/00—Systems using the reflection or reradiation of radio waves, e.g. radar systems; Analogous systems using reflection or reradiation of waves whose nature or wavelength is irrelevant or unspecified
    • G01S13/02—Systems using reflection of radio waves, e.g. primary radar systems; Analogous systems
    • G01S2013/0236—Special technical features
    • G01S2013/0245—Radar with phased array antenna

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  • Engineering & Computer Science (AREA)
  • Radar, Positioning & Navigation (AREA)
  • Remote Sensing (AREA)
  • Physics & Mathematics (AREA)
  • Computer Networks & Wireless Communication (AREA)
  • General Physics & Mathematics (AREA)
  • Electromagnetism (AREA)
  • Radar Systems Or Details Thereof (AREA)

Abstract

A system in a vehicle includes a radar system having a Uniform Linear Array (ULA) of antenna elements and a Uniform Rectangular Array (URA) of antenna elements to receive reflected signals generated by transmitted radio frequency energy. The ULA is arranged perpendicular to the URA. The processing circuitry estimates one or more elevation angles using the reflected signals received by the ULA of the antenna element and estimates an azimuth angle corresponding to each of the one or more elevation angles using the one or more elevation angles and the reflected signals received by the URA of the antenna element. Each of the one or more elevation angles and the corresponding one of the azimuth angles is referred to as an angle of arrival (AOA) of a reflected signal from the object. Control of vehicle operation is based on each AOA for each object.

Description

Multi-stage angle-of-arrival estimation in a vehicle radar system
Technical Field
The subject disclosure relates to multi-stage angle of arrival (AOA) estimation in a vehicle radar system.
Background
Vehicles (e.g., automobiles, trucks, construction equipment, farm equipment, automated factory equipment) increasingly use sensors to obtain information about the vehicle and its surroundings. Exemplary sensors to obtain information about the vehicle include an Inertial Measurement Unit (IMU) and a steering wheel angle sensor. Exemplary sensors to obtain information about the area surrounding the vehicle include cameras, radar systems, and lidar systems. This information may be helpful for semi-autonomous operation (e.g., adaptive cruise control, automatic braking), autonomous operation, or warning to the driver. Different sensors provide different information.
The radar system includes a transmitting element that transmits radio frequency energy. When the transmitted signal encounters an object, some of the energy is reflected back. The radar system provides range and AOA to each detected object and may also provide range rate (i.e., relative velocity or doppler) to each object. AOA refers to the angle (relative to the antenna boresight) at which each antenna receives the reflected signal. AOA estimation can be challenging when reflections are highly correlated. Accordingly, it is desirable to provide multi-stage AOA estimation in a vehicle radar system.
Disclosure of Invention
In an exemplary embodiment, a system in a vehicle includes a radar system. The radar system includes a Uniform Linear Array (ULA) of antenna elements that receive reflected signals generated by transmitted radio frequency energy, and a Uniform Rectangular Array (URA) of antenna elements that receive reflected signals generated by transmitted radio frequency energy, wherein the ULA of the antenna elements are arranged perpendicular to the URA of the antenna elements. The system also includes processing circuitry to estimate one or more elevation angles using the reflected signals received by the ULA of the antenna element, and estimate an azimuth angle corresponding to each of the one or more elevation angles using the one or more elevation angles and the reflected signals received by the URA of the antenna element. Each of the one or more elevation angles and the corresponding one of the azimuth angles is referred to as an angle of arrival (AOA) of a reflected signal from the object. The processing circuit also controls operation of the vehicle based on each AOA of each object.
In addition to one or more features described herein, the antenna elements of the ULA are located in the same (x, y) coordinate and different z coordinates in the [ x, y, z ] coordinate system.
In addition to one or more features described herein, the antenna elements of a URA are located in different (x, y) coordinates and the same z coordinate in rows and columns.
In addition to one or more features described herein, the antenna elements of the ULA are located [0, z [ ] i ]The antenna elements of the URA are located at [ x ] j ,y k ,0]Index i has a value of 1 to M, where M is the number of antenna elements of the ULA, and index j has a value of 1 to M l The index k has a value of 0 to M r Wherein the day of URAThe number of line elements being M l And M r The product of (a) and (b).
In addition to one or more features described herein, the processing circuitry uses the reflected signal received by the ULA of the antenna element to estimate one or more elevation angles by calculating each of the one or more elevation angles.
In addition to one or more features described herein, the processing circuitry calculates each of the one or more elevation angles based on a model of the calculated received signal.
In addition to one or more features described herein, the received signal model includes samples of reflected signals received by the antenna elements of the ULA and a complex normal noise vector.
In addition to one or more features described herein, the processing circuitry estimates an azimuth angle corresponding to each of the one or more elevation angles by calculating an azimuth angle corresponding to each of the one or more elevation angles.
In addition to one or more features described herein, the processing circuitry calculates an azimuth angle corresponding to each of the one or more elevation angles based on the calculated received signal model.
In addition to one or more features described herein, the received signal model includes samples of reflected signals received by the antenna elements of the URA and a complex normal noise vector.
In another exemplary embodiment, a method of assembling a system in a vehicle includes assembling a radar system. Assembling the radar system includes forming a Uniform Linear Array (ULA) of antenna elements to receive reflected signals generated by the transmitted radio frequency energy and forming a Uniform Rectangular Array (URA) of antenna elements to receive reflected signals generated by the transmitted radio frequency energy. Forming the ULA of the antenna element and the URA of the antenna element includes arranging the ULA of the antenna element perpendicular to the URA of the antenna element. The method also includes configuring the processing circuitry to estimate one or more elevation angles using the reflected signals received by the ULA of the antenna element, and to estimate an azimuth angle corresponding to each of the one or more elevation angles using the one or more elevation angles and the reflected signals received by the URA of the antenna element. Each of the one or more elevation angles and the corresponding one of the azimuth angles is referred to as an angle of arrival (AOA) of a reflected signal from the object. The processing circuit is further configured to control operation of the vehicle based on each AOA of each object.
In addition to one or more features described herein, forming the ULA of the antenna element in an [ x, y, z ] coordinate system includes positioning the antenna elements of the ULA at the same (x, y) coordinate and a different z coordinate.
In addition to one or more features described herein, forming the URA of antenna elements includes positioning the antenna elements of the URA in different (x, y) coordinates and the same z coordinate in rows and columns.
In addition to one or more features described herein, the antenna elements of the ULA are positioned at [0, z [ ] i ]Positioning the antenna elements of the URA at [ x ] j ,y k ,0]Index i has a value of 1 to M, where M is the number of antenna elements of the ULA, and index j has a value of 1 to M l The index k has a value of 0 to M r Wherein the number of antenna elements of the URA is M l And M r The product of (a).
In addition to one or more features described herein, configuring the processing circuitry includes the processing circuitry estimating the one or more elevation angles using reflected signals received by the ULA of the antenna element by calculating each of the one or more elevation angles.
In addition to one or more features described herein, configuring the processing circuitry includes the processing circuitry calculating each of the one or more elevation angles based on the calculated received signal model.
In addition to one or more features described herein, computing the received signal model includes the received signal model including samples of reflected signals received by the antenna elements of the ULA and a complex normal noise vector.
In addition to one or more features described herein, configuring the processing circuitry includes the processing circuitry estimating an azimuth angle corresponding to each of the one or more elevation angles by calculating an azimuth angle corresponding to each of the one or more elevation angles.
In addition to one or more features described herein, configuring the processing circuitry includes the processing circuitry calculating an azimuth angle corresponding to each of the one or more elevation angles based on the calculated received signal model.
In addition to one or more features described herein, computing the received signal model includes the received signal model including samples of reflected signals received by the antenna elements of the URA and a complex normal noise vector.
The above features and advantages and other features and advantages of the present disclosure will become apparent from the following detailed description when taken in conjunction with the accompanying drawings.
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Other features, advantages and details appear, by way of example only, in the following detailed description, the detailed description referring to the drawings in which:
FIG. 1 is a vehicle with a radar system that performs multi-stage angle of arrival (AOA) estimation in accordance with one or more embodiments;
FIG. 2 details aspects of a radar system for performing multi-stage AOA estimation in accordance with one or more embodiments; and
FIG. 3 is a flow diagram of a method of performing multi-stage AOA estimation in accordance with one or more embodiments.
Detailed Description
The following description is merely exemplary in nature and is not intended to limit the present disclosure, application, or uses. It should be understood that throughout the drawings, corresponding reference numerals indicate like or corresponding parts and features.
As described above, the radar system may be one of the sensors for acquiring the vehicle surrounding environment information. The angle of arrival (AOA) provided by a radar system is the angle at which the reflected signal reaches the antenna relative to the boresight of the antenna. Thus, the AOA represents the angle from the radar system to the reflecting object. When the reflected signals are highly correlated (i.e., very similar), it can be challenging to distinguish between the azimuth and elevation AOA components. Existing methods include estimating azimuth and elevation separately, and then pairing the elevation and corresponding azimuth estimates associated with the same reflection. Embodiments of the systems and methods herein relate to multi-stage AOA estimation in a vehicle radar system. A Uniform Linear Array (ULA) of antenna elements is used to estimate the elevation angle. A vertical Uniform Rectangular Array (URA) of antenna elements is used to estimate azimuth in a subsequent stage based on elevation estimation.
According to an exemplary embodiment, fig. 1 is a vehicle 100 having a radar system 110 that performs multi-stage AOA estimation. The exemplary vehicle 100 shown in fig. 1 is an automobile 101. In addition to radar system 110, vehicle 100 may include additional sensors 130 (e.g., cameras, lidar systems). The number and location of radar system 110 and additional sensors 130 is not limited by the exemplary illustration. The vehicle 100 also includes a controller 120. For example, controller 120 may obtain information from radar system 110 and one or more additional sensors 130 and use the information to control operation of vehicle 100. An exemplary object 140 (e.g., another vehicle 100, a pedestrian, a tree) is indicated, and a reflected signal R resulting from reflection of the emitted energy by the object 140 is also indicated. The AOA is shown relative to the antenna boresight b. In the two-dimensional view of fig. 1, AOA represents azimuth (in the xy plane) while elevation (between the xy plane and the z axis) is not visible.
Radar system 110 may include its own controller, and the processes involved in estimating AOA may be performed by the controller of radar system 110, controller 120, or a combination thereof. The controller of radar system 110 and controller 120 may include processing circuitry that may include an Application Specific Integrated Circuit (ASIC), electronic circuitry, a processor (shared, dedicated, or group) and memory that execute one or more software or firmware programs, combinational logic circuitry, and/or other suitable components that provide the described functionality.
FIG. 2 details aspects of radar system 110 for performing multi-stage AOA estimation in accordance with one or more embodiments. In particular, the antenna configuration is illustrated in terms of a position in meters (m) on an x, y, z coordinate system. A Uniform Linear Array (ULA) 205 of antenna elements 210 and a Uniform Rectangular Array (URA) 215 of antenna elements 210 are shown. In ULA205 there are M antenna elements 210. In the exemplary case shown in fig. 2, M =16. In the example shown, in the URA215, the number of rows Mr of antenna elements 210 is 12 and the number of columns Mc of antenna elements 210 is 4. Thus, in the exemplary case, the total number of antenna elements 210 in the URA215 is 48 (Mr × Mc). As shown, ULA205 is perpendicular to URA215. This relative positioning of ULA205 and URA215 is necessary to eliminate the azimuth component from the angle estimate obtained with ULA205, as described in detail with reference to fig. 3. All of the antenna elements 210 receive reflected energy from the radio frequency transmissions of the radar system 110.
FIG. 3 is a flow diagram of a method 300 of performing multi-stage AOA estimation in accordance with one or more embodiments. The process may be performed by processing circuitry within radar system 110, controller 120, or a combination of both. At block 310, the process includes obtaining a reflected signal at each antenna element 210 of ULA205 and URA215. At block 320, the process includes estimating an elevation angle based on the reflected signals R received at each antenna element 210 of ULA205, as described in detail. At block 330, the process includes estimating an azimuth angle corresponding to each elevation angle estimate obtained with ULA205 (at block 320) based on the reflected signals R received at each antenna element 210 of URA215, also as described in detail. Once the azimuth and elevation estimates (i.e., AOA estimates) are obtained (at blocks 320 and 330), those and other information from radar system 110 (e.g., range rate) may be used to perform autonomous or semi-autonomous control of vehicle 100 or to provide a warning to the driver about one or more objects 140 at block 340.
The reflected signal R received at each antenna element 210 forms a vector of signal replicas:
Figure BDA0003833492950000051
t in equation 1 represents the transposition. The number of reflected signals R received at each antenna element 210 is L, with an index k =1, 2. As previously mentioned, the L received reflected signals R may be highly correlated. Thus, conventional AOA estimation may not be feasible. The received signal model is given by:
Figure BDA0003833492950000052
in equation 2, y is expressed in the time sample t k Of the sampled signal (M + M) r x M l ) x 1 complex vector, phi is azimuth, theta is elevation, n (t) k ) Is expressed at a time sample t k Of additive noise of (M + M) r x M l ) x 1 complex vector. Statistically, the assumptions about the received reflected signal R and noise are:
S l (t k ) CN (0, C) [ equation 3]
n(t k )～CN(0,σ ω I) [ equation 4 ]]
In equations 3 and 4, CN represents a complex normal random vector with an average value of 0. The covariance matrix C in equation 3 is the lxl off-diagonal complex matrix, and in equation 4 the covariance matrix is the noise power σ ω And the product of the identity matrix I.
Also from equation 2:
Figure BDA0003833492950000061
generalized array response vector
Figure BDA0003833492950000062
Given by:
Figure BDA0003833492950000063
then, to facilitate array processing:
Figure BDA0003833492950000064
h in equation 7 represents the hermitian operator. In equations 6 and 7, the array radiation pattern G is given by:
Figure BDA0003833492950000065
each g is a complex gain associated with one of the M antenna elements 210 in the direction (theta, phi). The gain values may be obtained by calibrating each antenna element 210 prior to deployment in the radar system 110. This value reflects the antenna phase and gain in the presence of mutual coupling with other adjacent antenna elements 210 in ULA205 or URA215. If each antenna element 210 has equal gain in all directions (i.e., omnidirectional), then the radiation pattern G will be an identity matrix. In equation 6, the steering vector a is a vector of phase shifts of signals observed for signals transmitted from (θ, φ), expressed as:
Figure BDA0003833492950000066
in equation 9, each q m Is the position of the antenna element 210 on the x, y, z axis shown in fig. 2, the index m identifies the antenna element 210 in the ULA205 or URA215. Each position is given by:
Figure BDA0003833492950000067
where antenna element 210 is part of ULA205, the x and y coordinates are 0
Figure BDA0003833492950000071
As shown in fig. 2, or another constant. In the case of the antenna element 210 of the URA215, the z-coordinate is 0
Figure BDA0003833492950000072
As shown in fig. 2, or another constant. Also in equation 9, the phase shift vector u corresponding to each AOA of interest is given by:
Figure BDA0003833492950000073
using equations 9 and 11, for ULA205 (i.e., equation 11)
Figure BDA0003833492950000074
) Product u as part of equation 9 T q m Only the sin theta component of vector u will remain according to equation 11. That is, only the elevation angle θ remains. As such, reflected signals R received by ULA205 may be used to estimate an elevation angle θ at which each reflected signal R reaches each antenna element 210 of ULA 205. The elevation angle theta is between-pi/2 and pi/2.
Known algorithms can be used to obtain an estimate of the elevation angle theta. That is, each elevation angle θ estimate may be calculated as opposed to a grid search performed according to prior methods. For example, a multiple signal classification (MUSIC) -like algorithm (e.g., root-MUSIC) may be used to calculate the elevation angle θ i Wherein i = 1. The singular value decomposition of the covariance matrix, which is obtained using the snapshot and is composed of the reflected signals R received at the antenna elements 210 of ULA205, is obtained according to equation 2, the root-MUSIC algorithm. According to equation 1, for each of the M antenna elements 210 of ULA205, the unitary matrix resulting from the singular value decomposition includes components of L replicas.
For elevation angle theta i Can estimate the corresponding azimuth angle phi, as indicated by equation 11. Thus, there is no need to subsequently pair separately estimated azimuth and elevation angles, which is according to existing methods. The azimuth estimate phi may also be obtained using known algorithms. For example, an extension of MUSIC-like algorithms is the estimation of signal parameters by rational invariance techniques (ESPRIT). The singular value decomposition of the covariance matrix, which is obtained using the snapshot and is formed from the reflected signals R received at the antenna elements 210 of the URA215, is obtained according to equation 2, the esprit algorithm.
While the foregoing disclosure has been described with reference to exemplary embodiments, it will be understood by those skilled in the art that various changes may be made and equivalents may be substituted for elements thereof without departing from the scope thereof. In addition, many modifications may be made to adapt a particular situation or material to the teachings of the disclosure without departing from the essential scope thereof. Therefore, it is intended that the disclosure not be limited to the particular embodiments disclosed, but that the disclosure will include all embodiments falling within its scope.

Claims (10)

1. A system in a vehicle, comprising:
a radar system, comprising:
a Uniform Linear Array (ULA) of antenna elements configured to receive a reflected signal generated by transmitted radio frequency energy; and
a Uniform Rectangular Array (URA) of antenna elements configured to receive a reflected signal generated by transmitted radio frequency energy, wherein the ULA of the antenna elements is arranged perpendicular to the URA of the antenna elements; and
processing circuitry configured to estimate one or more elevation angles using reflected signals received by the ULA of the antenna element, estimate an azimuth angle corresponding to each of the one or more elevation angles using the one or more elevation angles and reflected signals received by the URA of the antenna element, wherein each of the one or more elevation angles and the respective one azimuth angle is referred to as an angle of arrival (AOA) of the reflected signals from the object, and control operation of the vehicle based on each AOA of each object.
2. The system of claim 1, wherein in [ x, y, z ]]In a coordinate system, the antenna elements of the ULA are located at the same (x, y) coordinate and different z coordinates, the antenna elements of the URA are located at different (x, y) coordinates and the same z coordinate in rows and columns, and the antenna elements of the ULA are located at [0, z coordinate i ]。
3. The system of claim 2, wherein the antenna elements of the URA are located at [ x [ ] j ,y k ,0]Index i has a value of 1 to M, where M is the number of antenna elements of the ULA, and index j has a value of 1 to M l The index k has a value of 0 to M r Wherein the number of antenna elements of the URA is M l And M r The product of (a).
4. The system of claim 1, wherein the processing circuitry is configured to estimate the one or more elevation angles using reflected signals received by the ULA of the antenna element by calculating each of the one or more elevation angles, the processing circuitry is configured to calculate each of the one or more elevation angles based on a calculated received signal model, and the received signal model comprises samples of reflected signals received by the antenna element of the ULA and a complex normal noise vector.
5. The system of claim 1, wherein the processing circuitry is configured to estimate an azimuth angle corresponding to each of the one or more elevation angles by computing an azimuth angle corresponding to each of the one or more elevation angles, the processing circuitry is configured to compute an azimuth angle corresponding to each of the one or more elevation angles based on a computed received signal model, and the received signal model comprises samples of reflected signals received by antenna elements of the URA and a complex normal noise vector.
6. A method of assembling a system in a vehicle, the method comprising:
assembling a radar system, comprising:
forming a Uniform Linear Array (ULA) of antenna elements configured to receive a reflected signal generated by the transmitted radio frequency energy; and
forming a Uniform Rectangular Array (URA) of antenna elements configured to receive reflected signals generated by the transmitted radio frequency energy, wherein forming the ULA of the antenna elements and the URA of the antenna elements includes arranging the ULA of the antenna elements perpendicular to the URA of the antenna elements; and
the processing circuitry is configured to estimate one or more elevation angles using reflected signals received by the ULA of the antenna element, estimate an azimuth angle corresponding to each of the one or more elevation angles using the one or more elevation angles and reflected signals received by the URA of the antenna element, wherein each of the one or more elevation angles and the respective one azimuth angle is referred to as an angle of arrival (AOA) of the reflected signals from the object, and control operation of the vehicle based on each AOA of each object.
7. The method of claim 6, wherein, in a [ x, y, z ] coordinate system, forming the ULA of the antenna element comprises positioning the antenna elements of the ULA at a same (x, y) coordinate and a different z coordinate, and forming the URA of the antenna element comprises positioning the antenna elements of the URA in rows and columns at a different (x, y) coordinate and the same z coordinate.
8. The method of claim 7, wherein the antenna elements of the ULA are positioned at [0, z i ]Positioning the antenna elements of the URA at [ x ] j ,y k ,0]Index i has a value of 1 to M, where M is the number of antenna elements of the ULA, and index j has a value of 1 to M l The index k has a value of 0 to M r Wherein the number of antenna elements of the URA is M l And M r The product of (a).
9. The method of claim 6, wherein configuring the processing circuitry comprises the processing circuitry estimating the one or more elevation angles using reflected signals received by the ULA of the antenna element by computing each of the one or more elevation angles, configuring the processing circuitry comprises the processing circuitry computing each of the one or more elevation angles based on a computed received signal model, and computing the received signal model comprises the received signal model comprising samples of reflected signals received by the antenna element of the ULA and a complex normal noise vector.
10. The method of claim 6, wherein configuring the processing circuitry comprises the processing circuitry estimating an azimuth angle corresponding to each of the one or more elevation angles by computing an azimuth angle corresponding to each of the one or more elevation angles, configuring the processing circuitry comprises the processing circuitry computing an azimuth angle corresponding to each of the one or more elevation angles based on computing a received signal model, and computing the received signal model comprises the received signal model comprising samples of reflected signals received by the antenna elements of the URA and a complex normal noise vector.
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